What three numbers have an average of 401?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 401. This means if we add these three numbers together and divide by 3, we should get 401.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 401 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 401 * 3 = x + y + z
- So, the sum of our three numbers should be: 1203
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1203.
Solution 1:
401, 401, 401
Verification:
(401 + 401 + 401) / 3 = 1203 / 3 ≈ 401
This solution is correct!
Solution 2:
401, 401, 401
Verification:
(401 + 401 + 401) / 3 = 1203 / 3 ≈ 401
This solution is correct!
Solution 3:
604, 560, 39
Verification:
(604 + 560 + 39) / 3 = 1203 / 3 ≈ 401
This solution is correct!
Solution 4:
520, 140, 543
Verification:
(520 + 140 + 543) / 3 = 1203 / 3 ≈ 401
This solution is correct!
Solution 5:
773, 354, 76
Verification:
(773 + 354 + 76) / 3 = 1203 / 3 ≈ 401
This solution is correct!
Explanation:
As you can see, there are many possible solutions. We can find more by:
- Choosing any two numbers
- Subtracting their sum from 1203 to get the third number
Remember:
- The numbers don't have to be whole numbers.
- They can even be negative (although that might not make sense in some real-world contexts).
- The order of the numbers doesn't matter for the average.